Maxima is a free and open-source computer algebra system that can perform symbolic computations such as solving equations, determining derivatives of functions, obtaining Taylor series, and manipulating algebraic expressions. In this article, I present the Maxima Bridge System, which is a collection of software programs that allows Stata to interface with Maxima so that Maxima can be used for symbolic computation to transfer data from Stata to Maxima and to retrieve results from Maxima. The cooperation between Stata and Maxima provides an environment for statistical analysis in which symbolic computation can be easily used together with all the facilities supplied by Stata. In this environment, symbolic computation algorithms can be used to manage the complexity of algebra and calculus, whereas numerical computation can be used when speed matters. I also discuss the software architecture of the Maxima Bridge System, and I present several examples to illustrate how to develop new Stata commands that exploit the capabilities of Maxima.